A Bigger Mathematical Picture for Computer Graphics

Eric Lengyel introduces geometric and Grassmann algebra as a unified mathematical framework for computer graphics, covering homogeneous coordinates, points, lines, and planes.

Slideshow & audio of Eric Lengyel’s keynote in the 2012 WSCG conference in Plzeň, Czechia, on geometric algebra for computer graphics. Timestamps: 0:00 Introduction 2:07 History 3:41 Outline of the talk 4:48 Grassmann algebra in 3-4 dimensions: wedge product, bivectors, trivectors, transformations 37:04 Homogeneous model 47:26 Practical applications: Geometric computation 56:27 Programming considerations 1:01:41 Summary Short abstract: "This talk introduces the basic concepts of the exterior algebra (aka geometric algebra or Clifford algebra) and presents a bigger mathematical picture that enables a deeper understanding of computer graphics concepts such as homogeneous coordinates for representing points, lines, and planes, the operations that can be performed among them using the progressive and regressive products, and incomplete pieces of the bigger picture, such as Plücker coordinates." ● Full abstract: wscg.zcu.cz/wscg2012/tutorial/f11-full.pdf ● Slides (pdf): terathon.com/wscg12_lengyel.pdf ● About the author: terathon.com/lengyel/ ● About geometric algebra: en.wikipedia.org/wiki/Geometric_algebra ● Some photos of the keynote: imgur.com/a/JrPRX Note: most of this information (including the video, available for both streaming and download as mp4) is available at the website of the Centre of Computer Graphics and Visualization of the University of West Bohemia: graphics.zcu.cz/seminars/?graphics_action=article&article_id…